Nuprl Lemma : rcp-Binet-Cauchy-corollary
∀[a,b:ℝ^3]. ((a x b)⋅(a x b) = ((a⋅a * b⋅b) - a⋅b * b⋅a))
Proof
Definitions occuring in Statement :
rcp: (a x b),
dot-product: x⋅y,
real-vec: ℝ^n,
rsub: x - y,
req: x = y,
rmul: a * b,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
rcp-Binet-Cauchy,
req_witness,
dot-product_wf,
false_wf,
le_wf,
rcp_wf,
rsub_wf,
rmul_wf,
real-vec_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
because_Cache,
independent_functionElimination,
isect_memberEquality
Latex:
\mforall{}[a,b:\mBbbR{}\^{}3]. ((a x b)\mcdot{}(a x b) = ((a\mcdot{}a * b\mcdot{}b) - a\mcdot{}b * b\mcdot{}a))
Date html generated:
2018_05_22-PM-02_42_49
Last ObjectModification:
2018_05_09-PM-01_38_42
Theory : reals
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